Gabriela is 32 years older than Luis. Gabriela and Luis first met 3 years ago. Eight years ago, Gabriela was 5 times older than Luis. How old is Gabriela now?
Solution: We can use the given information to write down two equations that describe the ages of Gabriela and Luis. Let Gabriela's current age be $g$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $g = l + 32$ Eight years ago, Gabriela was $g - 8$ years old, and Luis was $l - 8$ years old. The information in the second sentence can be expressed in the following equation: $g - 8 = 5(l - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $g$ , it might be easiest to solve our first equation for $l$ and substitute it into our second equation. Solving our first equation for $l$ , we get: $l = g - 32$ . Substituting this into our second equation, we get the equation: $g - 8 = 5($ $(g - 32)$ $ -$ $ 8)$ which combines the information about $g$ from both of our original equations. Simplifying the right side of this equation, we get: $g - 8 = 5g - 200$ Solving for $g$ , we get: $4 g = 192$ $g = 48$.